Problem: Ikta has an extraordinary feeling for undirected graphs. Ikta likes the undirected graph G and its two-point s, t pair (G, s, t) that has the greatest "beauty". The "beauty" of a pair (G, s, t) is the edge e = \\ {u, v \\} (u and v are two different points of G), and the shortest path from s to t in G. Is the number of things whose length is greater than the length of the shortest path from s to t in the undirected graph with g plus e.

Your job is to write a program that seeks its "beauty" given a pair (G, s, t).



Input

The input is given in the following format.

> N M s t
> x1 y1
> ...
> xi yi
> ...
> xM yM
>

First, the number of vertices, the number of edges, and the integers N, M, s, t representing the two vertices of the undirected graph are input. From the 2nd line to the M + 1th line, two vertices connected by edges are input. (However, let the set of G vertices be \\ {1, ..., N \\}.)

Constraints

Each variable being input satisfies the following constraints.

* 2 ≤ N ≤ 100,000
* 1 ≤ M ≤ 300,000
* 1 ≤ s, t, xi, yi ≤ N
* Different from s and t
* Guaranteed to reach t from s

Output

When the given graph is G, output the "beauty" of the set (G, s, t) in one line.

Examples

Input

3 2 1 3
1 2
2 3


Output

1


Input

9 8 7 8
2 6
4 9
8 6
9 2
3 8
1 8
8 5
7 9


Output

7


Input

4 3 1 4
1 2
3 4
4 1


Output

0


Input

9 7 8 9
9 6
6 5
3 6
3 7
2 5
8 5
1 4


Output

2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int INF = 1<<28;

typedef long long lli;

struct Edge {
  int v, w;
};

typedef vector<vector<Edge> > Graph;

vector<int> bfs(int src, const Graph &g) {
  const int n = g.size();
  vector<int> cost(n, INF);
  queue<int> que;
  cost[src] = 0;
  que.push(src);
  while(que.size()) {
    const int v = que.front();
    que.pop();
    for(int i = 0; i < g[v].size(); ++i) {
      int nv = g[v][i].v;
      if(cost[nv] != INF) continue;
      cost[nv] = cost[v] + 1;
      que.push(nv);
    }
  }
  return cost;
}

int main() {
  for(int N, M, s, t; cin >> N >> M >> s >> t; ) {
    --s; --t;
    Graph G(N);
    for(int i = 0; i < M; ++i) {
      int x, y; cin >> x >> y;
      --x; --y;
      G[x].push_back((Edge){y, 1});
      G[y].push_back((Edge){x, 1});
    }
    vector<int> cs = bfs(s, G);
    vector<int> ct = bfs(t, G);
    int mini = cs[t];
    sort(ct.begin(), ct.end());
    lli res = 0;
    for(int i = 0; i < N; ++i) {
      if(cs[i] == INF) continue;
      int target = mini - 2 - cs[i];
      res += upper_bound(ct.begin(), ct.end(), target)
        - lower_bound(ct.begin(), ct.end(), target);
    }
    cout << res << endl;
  }
  return 0;
}